-
作者：Beiglboeck, Mathias; Juillet, Nicolas
作者单位：University of Vienna; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：The basic problem of optimal transportation consists in minimizing the expected costs E[c(X-1, X-2)] by varying the joint distribution (X-1, X-2) where the marginal distributions of the random variables X-1 and X-2 are fixed. Inspired by recent applications in mathematical finance and connections with the peacock problem, we study this problem under the additional condition that (X-i)(i=1,2) is a martingale, that is, E[X-2 vertical bar X-1] = X-1. We establish a variational principle for this ...
-
作者：Czichowsky, Christoph; Schachermayer, Walter
作者单位：University of London; London School Economics & Political Science; University of Vienna
摘要：Given a sequence (M-n)(n=1)(infinity) of nonnegative martingales starting at M-0(n) = 1, we find a sequence of convex combinations (M-n)(n=1)(infinity) and a limiting process X such that (M-n)(n=1)(infinity) converges in probability to X-tau, for all finite stopping times tau. The limiting process X then is an optional strong supermartingale. A counterexample reveals that the convergence in probability cannot be replaced by almost sure convergence in this statement. We also give similar conver...
-
作者：Nourdin, Ivan; Nualart, David; Peccati, Giovanni
作者单位：Universite de Lorraine; University of Luxembourg; University of Kansas
摘要：We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39-64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460-3505], and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wie...
-
作者：Gouere, Jean-Baptiste; Marchand, Regine
作者单位：Universite de Orleans; Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：Consider a Boolean model Sigma in R-d. The centers are given by a homogeneous Poisson point process with intensity lambda and the radii of distinct balls are i.i.d. with common distribution nu. The critical covered volume is the proportion of space covered by Sigma when the intensity lambda is critical for percolation. Previous numerical simulations and heuristic arguments suggest that the critical covered volume may be minimal when nu is a Dirac measure. In this paper, we prove that it is not...
-
作者：Besalu, M.; Kohatsu-Higa, A.; Tindel, S.
作者单位：Universite de Lorraine; Universite de Lorraine; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter H. In the one-dimensional case with additive noise, our study encompasses all parameters H is an element of (0, 1), while the multidimensional case is restricted to the case H > 1/2. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.
-
作者：Friz, Peter K.; Gess, Benjamin; Gulisashvili, Archil; Riedel, Sebastian
作者单位：Technical University of Berlin; Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Chicago; University System of Ohio; Ohio University
摘要：We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11(1983) 46-57]. This condition is verified in many examples, even in absence of explicit expressions for the covariance or Volterra kernels. Of special interest are random Fourier series, with covariance given as Fourier series itself, and we formulate conditions direct...
-
作者：Guo, Xiaoqin
作者单位：Technical University of Munich
摘要：In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption that one of the following holds: (i) the environment is balanced and the perturbation satisfies a Kalikow-type ballisticity condition, (ii) the environment satisfies Sznitman's ballisticity condition. This is a generalized version of the Einstein relation for ...
-
作者：Kelly, David; Melbourne, Ian
作者单位：University of North Carolina; University of North Carolina Chapel Hill; New York University; University of Warwick
摘要：Consider an Ito process X satisfying the stochastic differential equation dX = a(X) dt + b(X) dW where a, b are smooth and W is a multidimensional Brownian motion. Suppose that W-n, has smooth sample paths and that Wn converges wealdy to W. A central question in stochastic analysis is to understand the limiting behavior of solutions X-n to the ordinary differential equation dX(n) = a(X-n) dt + b(X-n) dW(n). The classical Wong-Zakai theorem gives sufficient conditions under which X-n converges ...
-
作者：Fournier, Nicolas; Mischler, Stephane
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
摘要：We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials and Maxwell molecules. We establish a rate of propagation of chaos of the particle system to the unique solution of the Boltzmann equation. More precisely, we estimate the expectation of the squared Wasserstein distance with quadratic cost between the empirical measure of the particle system and the solution to the Boltzmann equation. The ...
-
作者：Harris, S. C.; Hesse, M.; Kyprianou, A. E.
作者单位：University of Bath; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0, K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the proc...
